## Homework Statement

When I'm trying to find the probability of finding an electron within a sphere of a certain radius, do i integrate the radial distribution probability function with respect to r from 0 to infinity? My book says the product of the radial distribution function times dr would give the probability, but I always thought you had to integrate it.

## Homework Equations

n/a just looking for a simple answer to my question... i didnt show the hw problem cos i wanna do it myself i just want this question answered.

## The Attempt at a Solution

I've attempted the problem, i just integrated and I wanna know if you should integrate.

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kuruman
Homework Helper
Gold Member
The probability of finding the particle in a shell of thickness dr having radius r is

$$dP=|\psi|^2\:4\pi r^2dr$$

The probability of finding the particle anywhere within a sphere of radius R is

$$P=\int^R_0 |\psi|^2\:4\pi r^2dr$$

Does this help?

yes! helps a ton! Thank you.

Notice that $$4\pi r^{2}$$ is the area of the surface of a sphere. This factor looks like that because you only have radial distribution, independent of azimuthal direction,
while if your wavefunction looks like $$\psi(r,\theta,\phi)$$ things will get a little more complicated, and will involve additional integrations.